Rotary electric machine

ABSTRACT

In a rotary electric machine, slots are formed between teeth of a stator core. A ratio of a number of poles to a number of slots is 2:3. When an electrical angle of a tooth tip width, which is a width dimension of a tip of each of the teeth in a circumferential direction of the stator, is represented by α, an electrical angle of a pole arc angle, which is an angle formed by two straight lines that connect a rotation center of a rotor to corners on a rotor surface side of one permanent magnet, is represented by β, and a number of pole pairs is represented by P, the tooth tip width is within a range of (electrical angle)±0.2°×P for a value that satisfies the following expression: β=−2.5α+319.7 (0&lt;β≤180) [deg].

TECHNICAL FIELD

The present invention relates to a concentrated winding rotary electricmachine using permanent magnets.

BACKGROUND ART

A motor for an electrified vehicle, for example, a hybrid vehicle, isdriven at RPM that is the same level as engine RPM (for example, 6,000r/min) or higher RPM (10,000 r/min or more) and hence has a feature ofwide operating range of RPM. As such a motor as being interposed betweenan engine and a transmission, a motor having a flat shape is preferred.Moreover, torque is generated by magnetic attraction force generatedbetween a stator and a rotor. The magnetic attraction force variesdepending on a position of the rotor, and hence when the varyingmagnetic attraction force matches a natural frequency of acircumferential portion of the stator of the motor, the motor generatesnoise.

Meanwhile, in a related-art permanent magnet rotary electric machine, arelationship between a tip width of each tooth of a stator and a pitchbetween magnets inserted in a rotor is numerically limited to reduce adistortion factor of a waveform of an induced voltage (see PatentLiterature 1, for example).

Moreover, in another related-art concentrated winding motor, two or morekinds of teeth having different gap lengths to a rotor surface areprovided in an axial direction of a stator to reduce noise near acarrier frequency (see Patent Literature 2, for example).

CITATION LIST Patent Literature

[PTL 1] JP 2002-101628 A

[PTL 2] JP 2002-112472 A

SUMMARY OF INVENTION Technical Problem

However, with the above-mentioned related-art rotary electric machines,vibrations caused by a variation in attraction force cannot besufficiently suppressed, and it is desired to reduce the vibrations moreefficiently.

The present invention has been made to solve the above-mentionedproblem, and therefore has an object to provide a rotary electricmachine, which is capable of suppressing vibrations caused by avariation in attraction force more efficiently.

Solution to Problem

According to one embodiment of the present invention, there is provideda rotary electric machine including: a stator including a stator core;and a rotor including a rotor core and a plurality of permanent magnets,which are fixed to the rotor core, the rotor being rotatable withrespect to the stator, the stator core including an annular core back,and a plurality of teeth, which project radially inward from the annularcore back, the stator core having slots formed between the plurality ofteeth, the rotary electric machine having a ratio of a number of polesto a number of slots of 2:3, wherein, when an electrical angle of atooth tip width, which is a width dimension of a tip of each of theplurality teeth in a circumferential direction of the stator, isrepresented by α, an electrical angle of a pole arc angle, which is anangle formed by two straight lines that connect a rotation center of therotor to corners on a rotor surface side of one of the plurality ofpermanent magnets, is represented by β, and a number of pole pairs isrepresented by P, the tooth tip width is within a range of (electricalangle)±0.2°×P for a value that satisfies the following expression:β=−2.5α+319.7 (0<β≤180) [deg].

Further, according to one embodiment of the present invention, there isprovided a rotary electric machine including; a stator including statorcore; and a rotor including a rotor core and a plurality of permanentmagnets, which are fixed to the rotor core, the rotor being rotatablewith respect to the stator, the stator core including an annular coreback, and a plurality of teeth, which project radially inward from theannular core back, the stator core having slots formed between theplurality of teeth, the rotary electric machine having a ratio of anumber of poles to a number of slots of 2:3, wherein, when an electricalangle of a tooth tip width, which is a width dimension of a tip of eachof the plurality of teeth in a circumferential direction of the stator,represented by α, an electrical angle of a pole arc angle, which is anangle formed by two straight lines that connect a rotation center of therotor to corners on a rotor surface side of one of the plurality ofpermanent magnets, is represented by β, and α and β that satisfy thefollowing expression: β=−2.5α+319.7 (0<β≤180) [deg] are represented byα1, and β1, respectively, β is β1, and wherein each of the plurality ofteeth is formed by combining, in an axial direction of the stator, aportion having a tooth tip width of γ1, which is smaller than α1 inelectrical angle, and a portion having a tooth tip width of γ2, which islarger than α1 in electrical angle.

Still further, according to one embodiment of the present invention,there is provided a rotary electric machine including: a statorincluding a stator core; and a rotor including a rotor core, and aplurality of permanent magnets, which are fixed to the rotor core, therotor being rotatable with respect to the stator, the stator coreincluding an annular core back, and a plurality of teeth, which projectradially inward from the annular core back, the stator core having slotsformed between the plurality of teeth, the rotary electric machinehaving a ratio of a number of poles to a number of slots of 2:3,wherein, when an electrical angle of a tooth tip width, which is a widthdimension of a tip of each of the plurality of teeth in acircumferential direction of the stator, is represented by α, anelectrical angle of a pole arc angle, which is an angle formed by twostraight lines that connect a rotation center of the rotor to corners ona rotor surface side of one of the plurality of permanent magnets, isrepresented by β, and α and β that satisfy the following expression:β=−2.5α+319.7 (0<β≤180) [deg] are represented by α1 and β1,respectively, β is β1, wherein each of the plurality of teeth is formedby combining, in an axial direction of the stator, portions having aplurality of kinds of different tooth tip widths, and wherein at leastone kind of tooth tip width has a minimum value in electrical angle thatis smaller than α1, and at least one kind of tooth tip width has amaximum value in electrical angle that is larger than α1.

Advantageous Effects of Invention

According to the rotary electric machine of the present invention, a 6fcomponent of an average value of attraction force of the teeth isreduced so that the vibrations caused by the variation in attractionforce can be suppressed.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a cross-sectional view perpendicular to an axial direction ofa rotary electric machine according to Embodiment 1 of the presentinvention.

FIG. 2 is a cross-sectional view for illustrating an enlarged part ofthe rotary electric machine of FIG. 1.

FIG. 3 is a graph for showing dependencies of attraction force of teethof respective phases and an average value of attraction force of threephases on a rotational position in Embodiment 1.

FIG. 4 is a graph for showing a dependency of a varying component of theattraction force on a tooth tip width when a pole arc angle of permanentmagnets is 128.1° in Embodiment 1.

FIG. 5 is a graph for showing a dependency of the varying component ofthe attraction force on the tooth tip width at each pole arc angle ofthe permanent magnets in Embodiment 1.

FIG. 6 is a graph for showing a relationship of a tooth tip width withwhich the varying component of the attraction force is minimized at eachpole arc angle of the permanent magnets in Embodiment 1.

FIG. 7 is a graph for showing a relationship between a component of theaverage value of the attraction force of the teeth and the tooth tipwidth when a relational expression of FIG. 6 is satisfied.

FIG. 8 is a cross-sectional view for illustrating a modification examplein which the permanent magnets of FIG. 2 are exposed to an outerperiphery of a rotor core.

FIG. 9 is a graph for showing a relationship between a tooth tip widthand a 6f component of an average value of attraction force of teeth whena pole arc angle of each permanent magnet of a rotary electric machineaccording to Embodiment 2 of the present invention is 128.1°.

FIG. 10 is a graph for showing differences among magnitudes of 6fcomponents of average values of the attraction force of the teethdepending on differences in tooth tip width.

FIG. 11 is a shape view in which a tooth tip width in electrical angleis 65° when the pole arc angle of each magnet is 128.1°.

FIG. 12 is a shape view in which a tooth tip width in electrical angleis 95° when the pole arc angle of each magnet is 128.1°.

FIG. 13 is an explanatory view for illustrating a first example of amethod of combining different tooth tip widths.

FIG. 14 is an explanatory view for illustrating a second example of themethod of combining different tooth tip widths.

FIG. 15 is an explanatory view for illustrating a third example of themethod of combining different tooth tip widths.

FIG. 16 is a shape view in which a tooth tip width in electrical angleis 61° when the pole arc angle of each magnet is 128.1°.

FIG. 17 is a shape view in which a tooth tip width in electrical angleis 69° when the pole arc angle of each magnet is 128.1°.

FIG. 18 is a shape view in which a tooth tip width in electrical angleis 100° when the pole arc angle of each magnet is 128.1°.

FIG. 19 is an explanatory view for illustrating a fourth example of themethod of combining different tooth tip widths.

FIG. 20 is an explanatory view for illustrating a fifth example of themethod of combining different tooth tip widths.

FIG. 21 is an explanatory view for illustrating a sixth example of themethod of combining different tooth tip widths.

FIG. 22 is a second graph for showing differences among magnitudes of 6fcomponents of average values of the attraction force of the teethdepending on differences in tooth tip width.

FIG. 23 is a graph for showing a relationship between a tooth tip widthand a 6f component of an average value of attraction force of teeth whena rotor of a rotary electric machine according to Embodiment 4 of thepresent invention is skewed.

FIG. 24 is a graph for showing a relationship between the tooth tipwidth and an optimal skew angle at which the 6f component of the averagevalue of the attraction force of the teeth is minimized when a pole arcangle of each permanent magnet is 128.1° in Embodiment 4.

FIG. 25 is a graph for showing a relationship between a shaft length ofa rotor core and a skew angle in Embodiment 4.

FIG. 26 is a graph for showing a modification example of a relationshipbetween the shaft length of the rotor core and the skew angle inEmbodiment 4.

FIG. 27 is a graph for showing a relationship between the tooth tipwidth and an optimal skew angle at which the 6f component of the averagevalue of the attraction force of the teeth is minimized when the polearc angle of each permanent magnet is changed.

FIG. 28 is a cross-sectional view for illustrating a modificationexample in which a tooth flange is horizontally asymmetrical.

FIG. 29 is a cross-sectional view for illustrating a modificationexample in which two permanent magnets are arranged for each pole.

DESCRIPTION OF EMBODIMENTS

Next, embodiments of the present invention are described with referenceto the drawings.

Embodiment 1

FIG. 1 is a cross-sectional view perpendicular to an axial direction ofa rotary electric machine according to Embodiment 1 of the presentinvention. In FIG. 1, the rotary electric machine includes a cylindricalstator 1, and a rotor 11, which is arranged inside the stator 1 to berotatable with respect to the stator 1. The stator 1 includes acylindrical stator core 2, and a plurality of windings (not shown),which are placed in the stator core 2.

The stator core 2 includes an annular core back 3, and a plurality of(in this example, 36) teeth 4, which project radially inward from thecore back 3. The teeth 4 are arranged at an equal pitch in acircumferential direction of the stator 1. A slot 6 is formed betweenadjacent teeth 4. In other words, the number of slots of the stator core2 is 36. Each winding is wound around the teeth 4 and inserted in theslots 6.

Phases of the windings are ordered as a U-phase, a V-phase, and aW-phase counterclockwise in FIG. 1. When torque is applied to a motor, athree-phase AC current having a phase difference of 120 degrees iscaused to pass through each phase.

The rotor 11 includes a cylindrical rotor core 12, and a plurality of(in this example, 24) permanent magnets 13, which are embedded and fixedin an outer periphery of the rotor core 12. An outer peripheral surfaceof the rotor core 12 is opposed to an inner peripheral surface of thestator core 2, that is, a tip surface of each tooth 4 via a gap.

The permanent magnets 13 are arranged at an equal pitch in acircumferential direction of the rotor 11. As each permanent magnet 13,a rectangular solid neodymium magnet is used, and one pole is formed ofone permanent magnet 13. The reference symbols “N” and “S”, which areillustrated in FIG. 1, indicate poles of the permanent magnets 13. Adirection of N-magnetic fluxes is a direction toward the outer peripheryof the rotor 11, and a direction of S-magnetic fluxes is a directionfrom the outer periphery to an inner periphery of the rotor 11. In theouter periphery of the rotor 11, magnetic poles having differentpolarities are alternately formed in the circumferential direction.

Moreover, at both ends of each permanent magnet 13 in thecircumferential direction of the rotor 11, flux barriers 14 configuredto suppress leakage of magnetic fluxes of the permanent magnets 13 areprovided. The rotary electric machine according to Embodiment 1 is aconcentrated winding motor having a ratio of the number of poles to thenumber of slots of 2:3.

FIG. 2 is a cross-sectional view for illustrating an enlarged part ofthe rotary electric machine of FIG. 1, and the stator 1 and the rotor 11for one pole pair are illustrated. At a distal end of each tooth 4, thatis, at an end of each tooth 4 on a radially inner side of the stator 1,a tooth flange 5 is provided. A width dimension of each tooth 4(dimension of each tooth 4 in the circumferential direction of thestator 1) in the tooth flange 5 is larger than a width dimension of aportion of each tooth 4 on the core back 3 side of the tooth flange 5.

At this time, an electrical angle of the width dimension of a tip ofeach tooth 4 including the tooth flange 5, that is, a tooth tip width,is represented by α. The electrical angle α is calculated, in a crosssection perpendicular to an axis of the rotary electric machine, as anangle formed by two straight lines that connect a rotation center of therotor 11 to both ends in a width direction of one tooth 4 in a directionof rotation of the rotor 11.

The electrical angle is a value obtained by multiplying a mechanicalangle by the number of pole pairs. In Embodiment 1, with the number ofpoles being 24 poles and the number of pole pairs being 12, a valueobtained by multiplying the angle between the two straight lines in thedirection of rotation, which is the mechanical angle, by 12 is α.

Similarly, an electrical angle of a pole arc angle of each permanentmagnet 13 excluding the flux barriers 14 is represented by β. Theelectrical angle β is calculated, in the cross section perpendicular tothe axis of the rotary electric machine, as an angle formed by twostraight lines that connect the rotation center of the rotor 11 tocorners on a rotor surface side (both ends in the circumferentialdirection of the rotor 11) of one permanent magnet 13 (one pole) in thedirection of rotation of the rotor 11. Therefore, as with thecalculation of the electrical angle α, a value obtained by multiplyingthe angle between the two straight lines in the direction of rotation,which is a mechanical angle, by 12 is β.

Next, noise generating factors in the concentrated winding motor havingthe ratio of the number of poles to the number of slots of 2:3, which isdescribed in Embodiment 1, are described first for a case in which anelectric current is not caused to pass through the windings.

When the rotor 11 is seen from each tooth 4, attraction force is changedwhen an N-pole is brought near and away from the tooth, and the same istrue for an S-pole. Therefore, when seen for teeth 4 of each phase, theattraction force varies twice for each rotation by 360° of theelectrical angle.

When the attraction force is seen for three teeth 4, timings at whichthe N-pole and the S-pole are brought near or away from the teeth aredifferent for each rotational position, and hence the attraction forcevaries six times for each rotation by 360° of the electrical angle.

The description has been given for the case in which the electriccurrent is not caused to pass through the windings. Similarly in a casewhere the electric current is caused to pass through the windings, arotating magnetic field of the N-pole and the S-pole is merely generatedby each tooth 4 in the direction of rotation of the rotor 11, and hencethe attraction force of the teeth 4 mainly varies six times for threeteeth 4.

Dependencies of the attraction force of the teeth 4 of respective phaseson the electrical angle at a time when the electric current is caused topass are shown in FIG. 3. In FIG. 3, a case in which a tip width of eachtooth 4 is 77.0° in electrical angle, and in which the pole arc angle ofeach permanent magnet 13 is 128.1° in electrical angle is shown.

As shown in FIG. 3, it can be seen that the attraction force is changedfor a phase difference of 120° among the U-phase, the V-phase, and theW-phase. Moreover, as for an average value of the attraction force ofthe phases, it can be seen that the average value varies six times foreach cycle of the electrical angle.

The average value of the attraction force of the phases refers toaverage attraction force with respect to the rotating magnetic field. Itis shown that, when the attraction force of the phases is sinusoidal,the average value of the attraction force is constant, that is, has novarying component. Therefore, when the average value of the attractionforce varies, the core back 3 and the teeth 4 vibrate.

Meanwhile, the stator core 2 is fixed to a frame or the like (notshown), and has a natural frequency depending on a deformation mode ofthe stator. The deformation mode refers to easiness of deformation at atime when force is applied in a plurality of directions for one cycle ofmechanical angle. For example, a deformation mode 2 indicates easinessof deformation into an elliptical shape. At this time, when the naturalfrequency of the frame or the like matches a time frequency of therotating magnetic field of the deformation mode 2, the frame resonatesto generate noise. Therefore, it is required to take noise reductionmeasures depending on each deformation mode.

As described above, in the 24-pole, 36-slot motor, which is described inEmbodiment 1, the average value of the attraction force varies six timesfor two poles and three slots. The deformation mode at this time is 0.The deformation mode 0 is a mode of a complete round shape in which theforce is increased or reduced uniformly irrespective of the rotationalposition, and when the attraction force has no varying component, themode does not match the natural frequency.

However, in a case where the varying component of the attraction forcepulsates as shown in FIG. 3, when the natural frequency of the frame orthe like of the deformation mode 0 matches the frequency of the varyingcomponent of the attraction force, the frame or the like resonates togenerate noise. The natural frequency of the deformation mode 0 is knownto be dependent on an outer diameter of the motor, and when the outerdiameter is increased, the natural frequency is reduced.

Next, in a case where the pole arc width β of each permanent magnet 13is 128.1° in electrical angle, the tip width α of each tooth 4 and anamplitude of the varying component of the average value of theattraction force of all teeth 4 are shown in FIG. 4. Here, the averagevalue of the attraction force of all teeth 4, which is shown in FIG. 3,can be expressed as Expression 1 below.

F=C+Σ _(i=1) ^(n)(A _(n) cos nθ+B _(n) sin nθ)   Expression 1

In Expression 1, F represents an average value of attraction force ofall teeth 4, C represents a DC component of the average value of theattraction force of all teeth 4, A_(n) represents cosine of an n-thorder component of the average value of the attraction force of allteeth 4, and B_(n) represents sine of the n-th order component of theaverage value of the attraction force of all teeth 4.

As shown in FIG. 3, with the varying component of the attraction forcevarying six times for each cycle of the electrical angle, the varyingcomponent of the average value of the attraction force is hereinafterdescribed as a 6th order component (6 f component). The letter “f”represents an electrical angle fundamental frequency, and is 1,000/60*(number of pole pairs (12))=200 Hz for 1,000 r/min, for example.

FIG. 4 is a graph in which, after the varying component of the averagevalue of the attraction force of the teeth is separated into sine andcosine by Fourier transform, sine, cosine, and a magnitude of the 6fcomponent are plotted for each tooth tip width. As shown in FIG. 4, atooth tip width with which the 6f component of the average value of theattraction force of the teeth is smallest is 77° in electrical angle.Moreover, tooth tip widths with which cosine and sine of the 6fcomponent of the average value of the attraction force of the teeth is 0are 78° and 71°, respectively, in electrical angle,

Further, in a method similar to that for FIG. 4, a relationship betweenthe tooth tip width and the 6f component of the average value of theattraction force of the teeth 4 for different pole arc angles β of eachpermanent magnet 13 is shown in FIG. 5. As shown in FIG. 5, it can heseen that, when the pole arc angle β of each permanent magnet 13 ischanged, an optimal value of the tooth tip width with which the 6fcomponent of the average value of the attraction force of the teeth 4 isminimized is changed. A result obtained by plotting optimal tooth tipwidths with which the magnitude of the 6f component of the average valueof the attraction force of the teeth 4 is minimized, which aredetermined from FIG. 5, is shown in FIG. 6.

As shown in FIG. 6, a relationship between the pole arc angle β of eachpermanent magnet 13 with which the magnitude of the 6f component of theaverage value of the attraction force of the teeth 4 is minimized andthe tooth tip width α can be expressed as β=−2.5α+319.7 [deg], and itcan be seen that the pole arc angle β and the tooth tip width α aresubstantially linearly proportional to each other.

Therefore, when the pole arc width β of each permanent magnet 13 isdetermined, the tooth tip width with which the 6f component of theaverage value of the attraction force of the teeth 4 is minimized can beuniquely determined, and the noise of the motor can be reduced.

Moreover, a relationship between the tip width of each tooth 4 and the6f component of the average value of the attraction force of the teeth 4at a time when the pole arc angle β of each permanent magnet 13 and thetip width α of each tooth 4 satisfy β=−2.5α+319.7 [deg] is shown in FIG.7. As shown in FIG. 7, the tooth tip width is minimized at around anelectrical angle of 72°, and the pole arc angle β of each permanentmagnet 13 at that time is 139.7° in electrical angle.

Through reduction of the 6f component of the average value of theattraction force of the teeth 4 described above, vibrations caused bythe variation in attraction force of the motor can be suppressed, andhence the noise of the motor can be reduced efficiently.

In FIG. 6, the relationship between the pole arc angle β of eachpermanent magnet 13 and the tooth tip width α is shown. However, it isrequired to take manufacturing tolerance into account, and the tooth tipwidth is within a range of (electrical angle)±0.2°×P (number of polepairs) for a value that satisfies β=−2.5α+319.7 [deg].

Moreover, in Embodiment 1, the case of 24 poles and 36 slots has beendescribed. However, in addition to 24 poles and 36 slots, similareffects can be obtained as long as the ratio of the number of poles tothe number of slots is 2:3.

Further, in Embodiment 1, the motor in which the permanent magnets 13are embedded in the rotor core 12 has been described. However, similareffects can be obtained also with a surface magnet rotor in which thepermanent magnets 13 are exposed to the outer periphery of the rotorcore 12 as illustrated in FIG. 8.

Embodiment 2

Next, Embodiment 2 of the present invention is described. The basicstructure of a rotary electric machine according to Embodiment 2 issimilar to that of FIG. 1. In Embodiment 2, when α and β that satisfythe following expression: β=−2.5α+319.7 (0<β≤180) [deg] are representedby α1 and respectively, β is β1, and each tooth 4 is formed bycombining, in an axial direction of the stator 1, a portion having atooth tip width of γ1, which is smaller than α1 in electrical angle, anda portion having a tooth tip width of γ2, which is larger than α1 inelectrical angle.

Moreover, when an average value of radial attraction force generated byall teeth 4 is represented by F1, the least common multiple of thenumber of poles and the number of slots is represented by S1, and whenvarying components of an (S1/P)-th order of the radial attraction forceare separated into cosine and sine for each of the tooth tip widths γ1and γ2, tooth tip widths with which absolute values of cosine and sineare minimized are represented by δ1 and δ2, respectively, an electricalangle of the tooth tip widths δ1 and δ2 that is smaller than the polearc angle of each permanent magnet 13 is represented by Amin, and anelectrical angle of the tooth tip widths δ1 and δ2 that is larger thanthe pole arc angle is represented by Amax, (tooth tip width γ1)<Amin,and Amax<(tooth tip width γ2).

Further, when magnitudes of change amounts of the (S1/P)-th order ofradial attraction force of cosine or sine of the varying components ofthe (S1/P)-th order of the radial attraction force generated by allteeth 4 that is larger in change amount when the tooth tip width isvaried are represented by Fγ1 and −Fγ2, the portion of γ1 and theportion of γ2 are stacked such that thicknesses of the portion of γ1 andthe portion of γ2 in a shaft length direction have a ratio of|Fγ2|:|Fγ1|.

FIG. 9 is a graph for showing a relationship between the tooth tip widthand the 6f component of the average value of the attraction force of theteeth 4 when the pole arc angle β of each permanent magnet 13 of therotary electric machine according to Embodiment 2 is 128.1°, and isobtained by additionally depicting values of the electrical angles 65°(γ1) and 95° (γ2) in FIG. 4.

In Embodiment2, different tooth tip widths are combined in the axialdirection to reduce the 6f component of the average value of theattraction force of the teeth 4. When the 6 f component of the averagevalue of the attraction force of the teeth 4 is seen in FIG. 9, there isan angle with which cosine or sine is 0. As described also in Embodiment1, when an electrical angle with which cosine is 0 is defined as δ2, andan electrical angle with which sine is 0 is defined as δ2, those valuesare δ1=78° and δ2=71°.

Those values are changed depending on the pole arc angle β of eachmagnet. Moreover, when a smaller one of δ1 and δ2 is defined as Amin,and a larger one of δ1 and δ2 is defined as Amax, Amin=71° and Amax=78°in this example.

For example, in a case where the pole arc angle of each magnet is 128.1°in electrical angle (shown in FIG. 9), a consideration is made ofcombining an electrical angle of 65° with which the tooth tip width issmaller than Amin and an electrical angle of 95° with which the toothtip width is larger than Amax. When the tooth tip width is smaller thanAmin, as shown in FIG. 9, cosine of the 6f component of the averagevalue of the attraction force of the teeth 4 is in a positive region,and sine is in a negative region. Meanwhile, when the tooth tip width islarger than Amax, cosine of the 6 f component of the average value ofthe attraction force of the teeth is in the negative region, and sine isin the positive region. Therefore, when both are combined in the axialdirection, cosine and sine of the 6f component of the average value ofthe attraction force of the teeth 4 are canceled by each other.

In FIG. 10, with the pole arc angle of each magnet being 128.1° inelectrical angle, respective magnitudes of 6f components of averagevalues of the attraction force of the teeth 4 for a case in which thetooth tip width is 65° in electrical angle, a case in which the toothtip width is 95° in electrical angle, a case in which the tooth tipwidths of 65° and 95° in electrical angle are combined, and a case inwhich the tooth tip width is 77° in electrical angle are shown.

The vertical axis indicates the 6f components of the average values ofthe attraction force of the teeth 4 that are standardized on the valueof 77° in electrical angle. For the case in which the electrical angleof 65° and the electrical angle of 95° are combined, a case in which aratio of lengths of the teeth 4 in the axial direction of the stator 1is 2:1 for the electrical angle 65° and the electrical angle 95°.

As shown in FIG. 10, the 6f components for the case in which the toothtip width is 65° in electrical angle and the case in which the tooth tipwidth is 95° in electrical angle are as large as 3.9 and 7.3 times the6f component for the case of an optimal tooth tip width of 77°,respectively. In contrast, the 6 f components for the case in which theelectrical angle of 65° and the electrical angle of 95° are combined ina stacking ratio of 2:1 is half the 6f component for the case in whichthe tooth tip width is 77° or less.

From the above description, through combining the portion in which thetooth tip width is smaller than Amin in electrical angle and the portionin which the tooth tip width is larger than Amax in electrical angle,the 6f components of the average values of the attraction force of theteeth 4 as a whole can be canceled by each other, and the noise of themotor can be reduced efficiently.

In Embodiment 2, the values with which cosine and sine of the 6fcomponent of the average value of the attraction force of the teeth 4are 0 are calculated to reduce the noise of the motor more effectively.However, also when the tooth tip width γ1 that is smaller than the toothtip width α and the tooth tip width γ2 that is larger than the tooth tipwidth α, which are shown in the relationship between the pole arc angleβ of each permanent magnet 13 and the tooth tip width α, which is shownin FIG. 6, are combined, because of the different phases of the 6fcomponents of the average values of the attraction force of the teeth,the 6f component of the average value of the attraction force of theteeth 4 can be reduced.

Moreover, in Embodiment 2, as a method of combining the tooth tip widthsof different electrical angles, the tooth tip widths have been combinedsuch that the 6f component of the average value of the attraction forceof the teeth 4 is minimized. However, of cosine and sine shown in FIG.9, tooth tip widths having change amounts of the 6f component of theaverage value of the attraction force of the teeth 4 that are largerthan the tooth tip width may be combined. In the case of FIG. 9, cosineof the 6f component of the average value of the attraction force of theteeth 4 is larger than sine in change amount, and hence when combinedwith a ratio of cosine, the tooth tip widths can be combined moreeffectively and easily.

Now, FIG. 11 and FIG. 12 are shape views in a case where the tooth tipwidth is 65° (γ1) in electrical angle and a case where the tooth tipwidth is 95° (γ2) in electrical angle. For example, in a case wherecosine values of the 6f components of the average values of theattraction force of the teeth for the tooth tip width γ1 and the toothtip width γ2 have magnitudes of 1:2 and phases that are 180° opposite,when the tooth tip width γ1 and the tooth tip width γ2 are combined inthe shaft length direction with a ratio of shaft lengths of 2:1, the 6fcomponent of the average value of the attraction force of the teeth 4 isreduced.

As the method of combining in this case, a portion 21 of the tooth tipwidth γ1 and a portion 22 of the tooth tip width γ2 may be divided atone point in the shaft length direction as illustrated in FIG. 13, ormay be divided at two or more points as illustrated in FIG. 14 or FIG.15. In other words, any ratio of shaft lengths at which the 6f componentof the average value of the attraction force of the teeth 4 is minimizedmay be set when considered as an entire shaft length.

In Embodiment 2, the optimal skew angle of 72 degrees or more has beenconsidered. However, dimensional tolerance is generated duringmanufacture, and hence a difference of ±0.2 degree in mechanical angle(2.4 degrees in electrical angle) may occur in an actual shape of themachine.

Moreover, the change amounts Fγ1 and Fγ2 of the (S1/P)-th order of theradial attraction force correspond to a positive value and a negativevalue, respectively.

Embodiment 3

Next, Embodiment 3 of the present invention is described. The basicstructure of a rotary electric machine according to Embodiment 3 issimilar to that of FIG. 1.

FIG. 16 is a shape view in which a tooth tip width in electrical angleof 61° (ϵ1) when the pole arc angle of each magnet is 128.1°, FIG. 17 isa shape view in which a tooth tip width in electrical angle of 69° (ϵ22)when the pole arc angle of each magnet is 128.1°, and FIG. 18 is a shapeview in which a tooth tip width in electrical angle of 100° when thepole arc angle of each magnet is 128.1° (ϵ3).

In Embodiment 3, there is adopted a configuration in which three kindsof tooth tip widths: ϵ1, ϵ2, and ϵ3 are used, and portions of therespective tooth tip widths are combined in the axial direction of thestator 1. The tooth tip widths have the following size relationship:ϵ1<ϵ2<ϵ3.

Now, an average value of radial attraction force generated by all teeth4 is represented by H. Moreover, the least common multiple of the numberof poles and the number of slots is represented by S1. Further, whenvarying components of the (S1/P)-th order of the radial attraction forceare separated into cosine and sine for each tooth tip width, tooth tipwidths with which absolute values of cosine and sine are minimized arerepresented δ1 and δ2, respectively. Still further, an electrical angleof the tooth tip widths δ1 and δ2 that is smaller than the pole arcangle of each permanent magnet 13 is represented by Amin, and anelectrical angle of the tooth tip widths δ1 and δ2 that is larger thanthe pole arc angle is represented by Amax. At this time, the tooth tipwidths satisfy the relationships: ⊖1<Amin and Amax<ϵ3 for the pole arcangle of each permanent magnet 13.

As the method of combining the portions, as illustrated in FIG. 19, aportion 31 of the tooth tip width ϵ1, a portion 32 of the tooth tipwidth ϵ2, and a portion 33 of the tooth tip width ϵ2 may be separated attwo points in the shaft length direction. Moreover, as illustrated inFIG. 20, those portions may be combined by being separated at three ormore points In other words, any ratio of shaft lengths at which the(S1/P)-th order component of the average value of the attraction forceof the teeth 4 is minimized may be set when considered as the entireshaft length. For example, when K kinds of portions of different toothtip widths are combined, any ratio may be set as long as Expression 2below is minimized.

$\begin{matrix}{H = {\sum\limits_{j = 1}^{K}{L_{j}{G_{j}( {{\cos \frac{S\; 1}{P}\theta_{j}} + {\sin \frac{S\; 1}{P}\theta_{j}}} )}}}} & {{Expression}\mspace{14mu} 2}\end{matrix}$

In Expression 2, H represents an (S1/P)-th order component of an averagevalue of the attraction force of all teeth 4. Moreover, G_(j) representsan (S1/P)-th order component of the average value of the attractionforce of all teeth 4 for the j-th tooth tip width of the K kinds ofportions having the different tooth tip widths. Further, L_(j)represents a stacking thickness of the j-th tooth top width of the Kkinds of portions having the different tooth tip widths.

For example, in a case where values obtained by combining sine andcosine of the (S1/P)-th order components of the average values of theattraction force of the teeth having the tooth tip width ϵ1, the toothtip width ϵ2, and the tooth tip width ϵ3 are minimized at magnitudes of1.5:0.5:1, when the tooth tip width ϵ1, the tooth tip width ϵ2, and thetooth tip width ϵ3 are combined in the shaft length direction with aratio of shaft lengths of 1.5:0.5:1 as illustrated in FIG. 21, the(S1/P)-th order component of the average value of the attraction forceof the teeth 4 is reduced.

In FIG. 22, with the pole arc angle of each magnet being 128.1° inelectrical angle, respective magnitudes of (S1/P)-th order components ofaverage values of the attraction force of the teeth 4 for a case inwhich the tooth tip width is 61° in electrical angle, a case in whichthe tooth tip width is 69° in electrical angle, a case in which thetooth tip width is 100° in electrical angle, a case in which the toothtip widths of 61°, 69°, and 95° in electrical angle are combined, a casein which the tooth tip widths of 65° and 95° in electrical angle arecombined, and a case in which the tooth tip width is 77° in electricalangle are shown.

The vertical axis indicates the (S1/P)-th order components of theaverage values of the attraction force of the teeth 4 that arestandardized on the value of 77° in electrical angle. For the case inwhich the electrical angle of 61°, the electrical angle of 69°, and theelectrical angle of 100° are combined, a case in which a ratio oflengths of the teeth 4 in the axial direction of the stator 1 is1.5:0.5:1 for the electrical angle 65°, the electrical angle 69°, andthe electrical angle of 100°. For the case in which the electrical angleof 65° and the electrical angle of 95° are combined, a case in which theratio of lengths of each tooth 4 in the axial direction of the stator 1is set to 2:1 for the electrical angle of 65° and the electrical angleof 95°.

As shown in FIG. 22, the (S1/P)-th order component in the case where theelectrical angle of 61°, the electrical angle of 69°, and the electricalangle of 100° are combined is reduced as compared to the case where theelectrical angle of 65° and the electrical angle of 95° are combined.

From the above description, through combining the portions of the threekinds of tooth tip widths, the (S1/P)-th order components of the averagevalues of the attraction force of the teeth 4 as a whole can be canceledby each other, and the noise of the motor can be reduced efficiently.

One kind of different tooth tip widths (γ2) may be a value thatsatisfies: β=−2.5α+319.7 [deg].

Moreover, in Embodiment 3, the portions of the three kinds of tooth tipwidths are combined such that both sine and cosine of the attractionforce of the teeth 4 are reduced. However, when portions of a largernumber of kinds of tooth tip widths are combined, effects that arelarger than those obtained when the three kinds of portions are combinedcan be obtained.

Further, when the stator 1 has a divided tooth structure of beingdivided for each tooth 4 in the circumferential direction, the tooth tipwidth can be set without being constrained by an arrangement, a shape,and the like of the windings, and the portions can be combined moreeffectively.

Embodiment 4

Next, Embodiment 4 of the present invention is described. The basicstructure of a rotary electric machine according to Embodiment 4 issimilar to that of FIG. 1. In Embodiment 4, the rotor 11 is skewed in aplurality of steps in the axial direction thereof. A skew angle of therotor 11 is 72 degrees or more and 180 degrees or less in electricalangle when seen as the entire shaft length of the rotor 11.

FIG. 23 is a graph for showing, in a case where a pole arc angle β ofeach permanent magnet 13 of the rotary electric machine according toEmbodiment 4 is 128.1°, a relationship between the 6f component of theaverage value of the attraction force of the teeth 4 when the rotor 11is skewed such that the 6f component of the average value of theattraction force of the teeth 4 is minimized, and the tooth tip width.

From FIG. 23, a value of cosine of the 6f component of the average valueof the attraction force of the teeth 4 is substantially reduced to 0.Meanwhile, a value of sine has a minimum value with respect to the toothtip width, and a minimum value of the amplitude is located at around thetooth tip width of 88°.

Moreover, a relationship between an optimal skew angle and the tooth tipwidth in FIG. 23 is shown in FIG. 24. As shown in FIG. 24, as the toothtip width becomes larger, the optimal skew angle is tangent to 72degrees, which is a theoretical skew angle of 5f , and it can be seenthat as the tooth tip width becomes smaller, the optimal skew anglebecomes larger.

Definition of the skew angle is described with reference to FIG. 25. Theskew angle as described in Embodiment 4 is an angle over the entireshaft length direction that is expressed in electrical angle. Forexample, in two-step skew shown in FIG. 25, when a shaft length of therotor core 12 is represented by 2a, and in a case where the skew angleis set to 0° in a range of from 0 to a, and the skew angle is set to 40°in a range of from a to 2a (straight line in FIG. 28) , the skew angleis a skew angle per shaft length of 2a (this time, 80 degrees inelectrical angle) as indicated by the broken line. The case of two-stepskew is described this time, but an equivalent value is obtained alsowhen the number of skew steps is three or more.

Moreover, as a method of skewing, the skew angle may not be uniformlyincreased as shown in FIG. 26. In the case of FIG. 26, a shaft lengthfor the skew angle of 0° is a, and a shaft length for the skew angle of40° is also a. Therefore, when a small skew angle and a large skew angleare combined, the entirety is the same as that of FIG. 24, and the skewangle is expressed as 80 degrees in electrical angle.

In FIG. 27, optimal skew angles for cases in which the pole arc angle ofeach permanent magnet 13 is changed are shown. As in FIG. 25, it can beseen that, even when the pole arc angle is changed, the optimal skewangle is 72 degrees or more.

In Embodiment 4, one kind of tooth tip width has been considered, buteven in a case where a plurality of tooth tip widths are combined asdescribed in Embodiments 2 and 3, when the optimal skew angle is set to72 degrees or more, 6f of the average value of the attraction force ofthe teeth 4 can be reduced.

Moreover, in Embodiments 1 to 4, the case in which the tooth flange 5 isprovided horizontally symmetrically with respect to one tooth 4 has beendescribed. However, the tooth flange 5 may be asymmetric with respect toa center line in the width direction of the tooth 4 as illustrated inFIG. 28, for example, and similar effects can be obtained also in thiscase.

Further, in Embodiments 1 to 4, the case in which one permanent magnet13 is provided for each pole has been described. However, two permanentmagnets 13 may be provided in a V shape for each pole as illustrated inFIG. 29, for example, and similar effects can be obtained also in thiscase. A pole arc angle β of the magnets in this case is, as illustratedin FIG. 29, a value obtained by multiplying an angle in the direction ofrotation between two straight lines that connect both ends on a radiallyouter side of the rotor to the rotation center by the number of polepairs (12).

REFERENCE SIGNS LIST

1 stator, 2 stator core, 3 core back, 4 tooth, 6 slot, 11 rotor, 12rotor core, 13 permanent magnet

1. A rotary electric machine, comprising: a stator including a statorcore; and a rotor including a rotor core and a plurality of permanentmagnets, which are fixed to the rotor core, the rotor being rotatablewith respect to the stator, the stator core including an annular coreback, and a plurality of teeth, which project radially inward from theannular core back, the stator core having slots formed between theplurality of teeth, the rotary electric machine having a ratio of anumber of poles to a number of slots of 2:3, wherein, when an electricalangle of a tooth tip width, which is a width dimension of a tip of eachof the plurality of teeth in a circumferential direction of the stator,is represented by α, an electrical angle of a pole arc angle, which isan angle formed by two straight lines that connect a rotation center ofthe rotor to corners on a rotor surface side of one of the plurality ofpermanent magnets, is represented by β, and a number of pole pairs isrepresented by P, the tooth tip width is within a range of (electricalangle)±0.2°×P for a value that satisfies the following expression:β=−2.5α+319.7 (0<β≤180) [deg].
 2. A rotary electric machine, comprising:a stator including a stator core; and a rotor including a rotor core anda plurality of permanent magnets, which are fixed to the rotor core, therotor being rotatable with respect to the stator, the stator coreincluding an annular core back, and a plurality of teeth, which projectradially inward from the annular core back, the stator core having slotsformed between the plurality of teeth, the rotary electric machinehaving a ratio of a number of poles to a number of slots of 2:3,wherein, when an electrical angle of a tooth tip width, which is a widthdimension of a tip of each of the plurality of teeth in acircumferential direction of the stator, is represented by α, anelectrical angle of a pole arc angle, which is an angle formed by twostraight lines that connect a rotation center of the rotor to corners ona rotor surface side of one of the plurality of permanent magnets, isrepresented by β, and α and β that satisfy the following expression:β=−2.5α+319.7 (0<β≤180) [deg] are represented by α1 and β1,respectively, β is β1, and wherein each of the plurality of teeth isformed by combining, in an axial direction of the stator, a portionhaving a tooth tip width of γ1, which is smaller than α1 in electricalangle, and a portion having a tooth tip width of γ2, which is largerthan α1 in electrical angle.
 3. The rotary electric machine according toclaim 2, wherein, when an average value of radial attraction forcegenerated by all of the plurality of teeth is represented by F1, a leastcommon multiple of the number of poles and the number of slots isrepresented by S1, a number of pole pairs is represented by P, and whenvarying components of an (S1/P)-th order of the radial attraction forceare separated into cosine and sine for each of the tooth tip widths γ1and γ2, tooth tip widths with which absolute values of cosine and sineare minimized are represented by δ1 and δ2, respectively, an electricalangle of the tooth tip widths δ1 and δ2 that is smaller than the polearc angle of each of the plurality of permanent magnets is representedby Amin, and an electrical angle of the tooth tip widths δ1 and δ2 thatis larger than the pole arc angle is represented by Amax, the followingexpressions are satisfied:γ1<Amin; andAmax<γ2.
 4. The rotary electric machine according to claim 3, wherein,when magnitudes of change amounts of the (S1/P)-th order of radialattraction force of cosine or sine of the varying components of the(S1/P)-th order of the radial attraction force that is larger in changeamount when the tooth tip width is varied are represented by Fγ1 and−Fγ2, the portion of γ1 and the portion of γ2 are stacked so thatthicknesses of the portion of γ1 and the portion of γ2 in a shaft lengthdirection have a ratio of |Fγ2|:|Fγ1|.
 5. A rotary electric machine,comprising: a stator including a stator core; and a rotor including arotor core, and a plurality of permanent magnets, which are fixed to therotor core, the rotor being rotatable with respect to the stator, thestator core including an annular core back, and a plurality of teeth,which project radially inward from the annular core back, the statorcore having slots formed between the plurality of teeth, the rotaryelectric machine having a ratio of a number of poles to a number ofslots of 2:3, wherein, when an electrical angle of a tooth tip width,which is a width dimension of a tip of each of the plurality of teeth ina circumferential direction of the stator, is represented by α, anelectrical angle of a pole arc angle, which is an angle formed by twostraight lines that connect a rotation center of the rotor to corners ona rotor surface side of one of the plurality of permanent magnets, isrepresented by β, and α and β that satisfy the following expression:β=−2.5α+319.7 (0<β≤180) [deg] are represented by α1 and β1,respectively, β is β1, wherein each of the plurality of teeth is formedby combining, in an axial direction of the stator, portions having aplurality of kinds of different tooth tip widths, and wherein at leastone kind of tooth tip width has a minimum value in electrical angle thatis smaller than α1, and at least one kind of tooth tip width has amaximum value in electrical angle that is larger than α1.
 6. The rotaryelectric machine according to claim 5, wherein, when an average value ofradial attraction force generated by all of the plurality of teeth isrepresented by F1, a least common multiple of the number of poles andthe number of slots is represented by S1, a number of pole pairs isrepresented by P, and when varying components of an (S1/P)-th order ofthe radial attraction force are separated into cosine and sine for eachof the plurality of kinds of different tooth tip widths, tooth tipwidths with which absolute values of cosine and sine are minimized arerepresented by δ1 and δ2, respectively, an electrical angle of the toothtip widths δ1 and δ2 that is smaller than the pole arc angle of each ofthe plurality of permanent magnets is represented by Amin, and anelectrical angle of the tooth tip widths δ1 and δ2 that is larger thanthe pole arc angle is represented by Amax, an electrical angle of atleast one kind of tooth tip width is smaller than Amin, and a maximumvalue of an electrical angle of at least one kind of tooth tip width islarger than Amax.
 7. The rotary electric machine according to claim 6,wherein, when respective thicknesses in a shaft length direction of theplurality of kinds of different tooth tip widths are represented by L1,L2, . . . , and LK, magnitudes of the varying components of the(S1/P)-th order of the radial attraction force are represented by G1,G2, . . . , and GK, phases are represented by θ1, θ2, . . . , and θK,and a value obtained by adding a thickness in the shaft length directionand cosine and sine of varying components of the (S1/P)-th order ofradial attraction force is represented by H, the plurality of kinds ofdifferent tooth tip widths are combined in the shaft length direction sothat H is minimized.
 8. The rotary electric machine according to claim1, wherein the rotor is skewed in a plurality of steps in an axialdirection thereof, and a skew angle of the rotor is an electrical angleof 72 degrees or more and 180 degrees or less when seen as an entireshaft length of the rotor.
 9. The rotary electric machine according toclaim 2, wherein the rotor is skewed in a plurality of steps in an axialdirection thereof, and a skew angle of the rotor is an electrical angleof 72 degrees or more and 180 degrees or less when seen as an entireshaft length of the rotor.
 10. The rotary electric machine according toclaim 5, wherein the rotor is skewed in a plurality of steps in an axialdirection thereof, and a skew angle of the rotor is an electrical angleof 72 degrees or more and 180 degrees or less when seen as an entireshaft length of the rotor.